High temperature superconducting cabon nanotubes and methods for making them

ABSTRACT

Disclosed are high temperature and/or room temperature superconducting carbon nanotube compositions having either a critical doping range, a critical chirality or a mixture thereof, high temperature superconducting graphite compositions having a critical doping range, methods of achieving a phase-coherent, near zero resistivity superconducting state in multiwalled carbon nanotubes and bundles of superconducting carbon nanotubes, methods of achieving a large positive magnetoresistance in bundles of superconducting carbon nanotubes, and methods for making and using such nanotubes or bundles. Disclosed also are devices and apparatuses (e.g., magnetic reading heads, magnetic switch devices, magnetic imaging devices, and superconducting quantum interference devices) comprising superconducting carbon nanotubes and/or bundles of superconducting carbon nanotubes.

RELATED APPLICATIONS

[0001] This application claims provisional priority to U. S. ProvisionalPatent Application Serial No. ______, filed 7 Aug. 2002.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to the general field ofsuperconductivity, material science, and engineering. This inventionrelates particularly to low dissipation or dissipation-free electricaltransport and the Meissner effect above room temperature in hightemperature superconducting nanotubes and to the method for making andusing same.

[0004] More particularly, the present invention relates to hightemperature superconducting carbon nanotube compositions having either acritical doping range, a critical chirality or a mixture thereof, tocompositions comprising single-walled nanotubes, multi-walled nanotubes,or mixtures or combination thereof and to compositions comprisingbundles of the aligned nanotubes, to methods of using aligned nanotubebundles, to wires or other conductors of electricity includingsuperconducting carbon nanotubes and aligned nanotube bundles, tomethods of making and using same, and methods to achieve aphase-coherent, near zero resistivity superconducting state insuperconducting nanotubes; to methods of achieving a large positivemagnetoresistance in bundles of superconducting carbon nanotubes; tomagnetic reading heads comprising superconducting carbon nanotubes; tomagnetic switch devices comprising superconducting carbon nanotubes; tomagnetic imaging devices comprising superconducting carbon nanotubes; tosuperconducting quantum interference devices comprising superconductingcarbon nanotubes. Many features of the materials including carbonnanotubes are a consequence of coherent (phase locked) superconductivityin carbon nanotubes that persist at temperatures even well above roomtemperature.

[0005] 2. Description of the Related Art

[0006] Superconductivity is a phenomenon displayed by certain conductorsthat demonstrate no resistance to the flow of an electric current.Superconductors also repel magnetic fields (Meissner effect).Superconductors have the ability to conduct electricity without the lossof energy. When current flows in an ordinary conductor, for examplecopper wire, some energy is lost. In a light bulb or electric heater,the electrical resistance creates light and heat. In metals such ascopper and aluminum, electricity is conducted as outer energy levelelectrons migrate as individuals from one atom to another. These atomsform a vibrating lattice within the metal conductor; the warmer themetal the more it vibrates. As the electrons begin moving through themaze, they collide with tiny impurities or imperfections in the latticeor lattice vibrations. When the electrons bump into these obstacles theyfly off in all directions and lose energy in the form of heat.

[0007] Inside a superconductor, the behavior of electrons is vastlydifferent. The impurities and lattice are still there, but the movementof the superconducting electrons through the obstacle course is quitedifferent. As the superconducting electrons travel through the conductorthey pass unobstructed through the complex lattice. Because they bumpinto nothing and create no friction they can transmit electricity withno appreciable loss in the current and no loss of energy.

[0008] The ability of electrons to pass through superconducting materialunobstructed has puzzled scientists for many years. The warmer asubstance is the more it vibrates. Conversely, the colder a substance isthe less it vibrates. Early researchers suggested that fewer atomicvibrations would permit electrons to pass more easily. However thispredicts a slow decrease of resistivity with temperature. It soon becameapparent that these simple ideas could not explain superconductivity. Itis much more complicated than that.

[0009] Superconductivity is manifested only below a certain criticaltemperature called “T_(c)” and a critical magnetic field called “H_(c),”which vary with the material used. Before about 1986, the highest T_(c)that could be achieved was 23.2 K (−249.8° C./−417.6° F.) inniobium-germanium compounds. Such low temperatures were achieved by useof liquid helium, an expensive, inefficient coolant.Ultralow-temperature operations place a severe constraint on the overallefficiency of a superconducting machine. Thus, large-scale operation ofsuch machines has not been considered practical.

[0010] Following about 1986, discoveries began to radically alter thesituation. Ceramic copper-oxide compounds containing rare earth elementswere found to be superconductive at temperatures high enough to permitusing liquid nitrogen as a coolant. Because liquid nitrogen, at 77 K(−196° C./−321° F.), cools 20 times more effectively than liquid heliumand is 10 times less expensive, a variety of possible applicationssuddenly began to hold the promise of economic feasibility. In about1987, the composition of one of these superconducting compounds, with aT_(c) of 94 K (−179° C./−290° F.), was revealed to be YBa₂Cu₃O₇(yttrium-barium-copper-oxide). It has since been shown that rare-earthelements, such as yttrium, are not an essential constituent, and inabout 1988, a thallium-barium-calcium copper oxide was discovered with aT_(c) of 125 K (−148° C./−234° F.).

[0011] Because of their lack of resistance, superconductors have beenused to make electromagnets that generate large magnetic fields with noenergy loss. Superconducting magnets have been used in diagnosticmedical equipment, studies of materials, and in the construction ofpowerful particle accelerators. Using the quantum effects ofsuperconductivity, devices have been developed that measure electriccurrent, voltage, and magnetic field with unprecedented sensitivity. Thediscovery of better superconducting compounds is an important steptoward a far wider spectrum of applications, including faster computerswith larger storage capacities, nuclear fusion reactors in which ionizedgas is confined by magnetic fields, magnetic levitation (lifting orsuspension) of high-speed (“Maglev”) trains, and perhaps most importantof all, more efficient generation and transmission of electric power.

[0012] Although some cuprate systems are known to superconduct attemperature as high as 130 K, the ultimate goal of research into hightemperature superconductors is to find materials that superconduct at orabove room temperature (˜300 K). Thus, there is a need in the art forstable, easy to make and commercially viable room temperature (RT)superconducting materials. Nevertheless, finding RT superconductors is avery challenging problem in science. It was theoretically shown that RTsuperconductivity can not be realized within the conventionalphonon-mediated pairing mechanism. On the other hand, a theoreticalcalculation showed that superconductivity as high as 500 K can bereached through a pairing interaction mediated by undamped acousticplasmon modes in a quasi-one-dimensional electronic system. Moreover,high-temperature superconductivity can occur in a multi-layer electronicsystem due to an attraction of charge carriers in the same conductinglayer via exchange of virtual plasmons in neighboring layers. If thesetheoretical studies are relevant, one should be able to findhigh-temperature superconductivity in quasi-one-dimensional (1D) and/ormulti-layer systems.

[0013] Carbon nanotubes (discovered in 1991) constitute a novel class ofquasi-one-dimensional materials, which would offer the potential forhigh-temperature superconductivity. The simplest single walled nanotube(SWNT) consists of a single graphite sheet that is curved into a longcylinder, with a diameter which can be smaller than 1 nm. Band-structurecalculations predict that carbon nanotubes have two types of electronicstructures depending on the chirality, which is indexed by a chiralvector (n,m): n−m=3N+ν, where N, n, m are the integers, and ν=0, ±1. Thetubes with ν=0 are metallic while the tubes with ν=±1 aresemiconductive. The multi-walled nanotubes consist of at least twoconcentric shells which could have different chiralities. The MWNTspossess both quasi-one-dimensional and multi-layer electronicstructures. This unique quasi-one-dimensional electronic structure inboth SWNTs and MWNTs makes them ideal for plasmon-mediatedhigh-temperature superconductivity.

[0014] Indeed, in a series of five papers resident on the cond-mate-print archive since November 2001 (cond-mat/0111268; cond-mat/0208197;cond-mat/0208198; cond-mat/0208200; cond-mat/0208201), the inventorprovides over twenty arguments for room temperature superconductivity incarbon nanotubes. The one-dimensionality of the nanotubes complicatesthe right-of-passage for prospective quasi-one-dimensionalsuperconductors. The Meissner effect is less visible because thediameters of nanotubes are much smaller than the penetration depth. Zeroresistance is less obvious because of the quantum contact resistance andsignificant quantum phase slip, both of which are associated with afinite number of transverse conduction channels. Nonetheless, on-tuberesistance at room temperature has been found to be indistinguishablefrom zero for many individual multi-walled nanotubes.

[0015] It is known that the superconducting fluctuation inone-dimensional (1D) superconductors plays an essential role in theresistivity transition. A number of experiments have demonstrated alarge resistance well below T_(c) in thin superconducting wires.

[0016] Theories based on the quantum phase slips (QPS) can explain thefinite resistance in 1D superconductors. Essentially, the phase slips atlow temperatures are related to the macroscopic quantum tunneling (MQT),which allows the phase of the superconducting order parameter tofluctuate between zero and 2π at some points along the wire, resultingin voltage pulses. The QPS tunneling rate is proportional to exp(−S_(QPS)), where S_(QPS), in clean superconductors, is very close tothe number of transverse channels N_(Ch) in the limit of weak damping.If the number of the transverse channels N_(Ch) is small, the QPStunneling rate is not negligible, leading to a finite resistance at lowtemperatures. For a single-walled nanotube (SWNT), N_(Ch)=2, implying alarge QPS tunneling rate and thus a large resistance even if it is asuperconductor. For MWNTs with several metallic layers adjacent to eachother, the number of the transverse channels will increasesubstantially, resulting in the suppression of the QPS. If twosuperconducting tubes are closely packed together to effectivelyincrease the number of the channels, one would find a small resistanceat room temperature if the constituent tubes have a mean-field T_(c0)well above room temperature. This can naturally explain why on-tuberesistance at room temperature has been found to be indistinguishablefrom zero for many individual multi-walled nanotubes. This also providesan essential theoretical ground for developing arts to realize coherent,non-dissipative, and stable room temperature superconductivity in carbonnanotubes.

[0017] Definitions

[0018] Quantum phase slips are phenomena in which the phase coherence ismomentarily broken at some point in the superconductor, allowing a phaseslip to occur before phase coherence is reestablished.

[0019] Quasi-one-dimensional superconductors are superconductors withtransverse dimension far smaller than the superconducting coherentlength or superconductors where the electrons essentially move along onedirection.

[0020] Mean-field superconducting transition temperature is the criticaltemperature below which the electron pairing starts to take place.

[0021] Phase coherent superconducting state: A state with resistanceapproaching zero.

[0022] Phase incoherent superconducting state: Finite-resistance statebelow the mean-field superconducting temperature.

[0023] Meissner effect is a unique phenomenon of a superconductor: Amagnetic field can be expelled from the bulk of a superconductor whenthe field is cooled from a temperature above the superconductingtransition temperature.

[0024] Josephson coupling: Two superconducting materials that areseparated by an insulating or normal metal layer, or by a short, narrowconstriction can have a phase coherence between the two superconductingmaterials.

[0025] A nanotube is a small tube having a diameter between about 0.42and about 1000 nanometers.

[0026] A carbon nanotube (CNT) is a nanotube comprising substantiallyelemental carbon.

[0027] A multiwalled carbon nanotube (MWNT) is a collection of nestedCNTs which share a common axis.

[0028] A single walled carbon nanotube (SWNT) is a CNT comprising onlyone shell or layer.

[0029] A superconducting carbon nanotube (SCNT) is a CNT thatsuperconducts.

[0030] Doping is the process by which the electronic carrier density ischanged. Doping alters the overall electrical transport behavior. Likecuprate superconductors which can be doped into the superconductingstate or non-superconducting state, SCNTs can be doped to be optimallydoped superconductors, non-optimally doped superconductors or to benon-superconductors.

[0031] CNTs can either have a metallic or a semiconducting chirality. If(n−m) mod 3=0, the tube is said to have a metallic chirality. Otherwisethe tube's chirality is semiconducting. Technically, non-armchairmetallic chirality tubes have a small gap making them semiconducting.However, this gap is small. Because the Fermi level can easily be dopedoutside this small gap, the inventor ignores the semiconducting behaviorin this tube.

[0032] Both semiconducting and metallic chirality CNTs can be made tosuperconduct via the doping of carriers into the CNT.

[0033] Superconducting tubes are quasi-1D superconductors and can beJosephson coupled to exhibit less dissipation or resistivity.

[0034] Semiconducting tubes have a semiconducting chirality and have theFermi level between the valence and conduction band edge.

[0035] A straight CNT is parallel to another straight CNT, if the twoCNTs are aligned along the same direction. Such tubes will have a lengthl in common, where l is the minimum of the length of both tubes laidside-by-side. Over the distance l, one CNT will have analogous pointsthat are separated from analogous points on the second CNT, by the sameor nearly the same distance.

[0036] A CNT is proximate to another CNT, if the two CNTs are close toeach other. Proximity increases as more points on one CNT become closerto nearest points on the other CNT. For two straight CNTs which share alength l, proximity is maximized when the CNTs are parallel. Further, ifa difference in tube diameter s exceeds about 0.68 nm, the tubes willexhibit the greatest proximity if the tubes are nested over 1, i.e., thesmaller tube is inside the larger tube. If the difference in tubediameters for two SWNTs is less than about 0.68 nm, it may not bepossible to nest the tubes and proximity is maximized if the tubes areparallel and in contact over the length l.

[0037] Maximal proximity means CNTs arranged parallel with an optimal orminimized distance d between analogous points on the parallel disposedCNTs, i.e., d represents a minimized distance between analogous pointson the parallel disposed CNTs. Such superconducting tubes are said to bemaximally proximate superconducting carbon nanotubes (MPSCNTs). Aplurality or collection of CNTs are ‘maximally proximate’ when each tubeis maximally proximate each of its nearest neighbors. When the conceptof maximal proximity is directed to collections of tubes, thenmacro-conductive structures can be constructed. Because of the finitelength of a CNT, one CNT can begin near or before another CNT ends. Thuspercolation can arise from intertube coupling and create a macroscopiccontinuity even though the CNTs themselves are of a microscopicdimension.

[0038] If such proximate tubes are jointly shaped so that the tubes havethe same or similar separation along every point, but are not aligned ina straight line, then these tubes are also said to be parallel.

[0039] A coherent superconducting carbon nanotube line (CSCNTL) is acollection of superconducting carbon nanotubes (SCNTs) which exhibits agreater “phase coherence” (compared to the separated tubes) andtherefore a lower resistivity than exhibited by the separated tubes.MPSCNTs comprises a CSCNTL. For example, the collection of CNTscomprises CNTs of equal or nearly equal length where the ends of thetubes only are in electrical contact with each other. The net resistanceof the collection is smaller if the SCNTs are closer to each other.Proximity induces this superconducting synergy. The phase coherence is aresult of Josephson coupling between individual SCNTs that causes thenet resistance of two adjacent SCNTs to be less than the parallelcombination of their separated resistance.

[0040] This proximity induced synergy in SCNTs results in the formationof collections of SCNTs having a very low resistivity. A dc resistivityof less than 1 μOhm-cm is readily obtainable in aligned collections ofSCNTs. Thus, increasing the number of SCNTs that have maximal proximityin a collection of SCNTs results in more coherent superconductingtransport within the construct. Although individual superconductingSWNTs are not entirely phase coherent and therefore exhibit appreciabledissipation, when bundled together the collective resistance is muchless than the resistance found from an end to end combination ofindividual tubes. The greater the number of SCNTs that have maximalproximity in the collection, the greater the number of conductivechannels, and, therefore, the lower the contact resistance. Moreover,the more maximally proximate SCNTs in the collection, the lower thecollective and individual on-tube resistances. The net resistancedecreases as both the contact and on-tube resistances decrease.

[0041] Individual SCNTs, especially individual single-walled carbonnanotubes (SWCNTs), can exhibit a large amount of phase slipresistivity. The resistivity of these individual SWCNTs can changesignificantly when the SWCNTs are brought into maximal proximity duringthe construction of SCNTLs or CSCNTLs.

[0042] The term orphan superconducting carbon nanotube (OSCNT) means anySCNT having a resistivity that lowers appreciable when brought intomaximal proximity with another SCNT or superconductor. Thus, SCNTs areeither CSCNTs or OSCNTs. The distinction between an CSCNT and OSCNT israther qualitative, but the distinction is evidenced from a relativechange in superconducting properties as the isolated SCNT in question isbrought close to an isolated CSCNT. An OSCNT is therefore distinguishedfrom a CSCNT because an OSCNT exhibits a larger relative change inresistivity when brought near an CSCNT as compared to the change inresistivity when an CSCNT is brought near another CSCNT. For example,the resistivity of an OSCNT maybe reduced as much as about 60%, whilethe resistivity of an CSCNT maybe reduced only about 6%.

[0043] Bundling is the term given to the mutual placement of CNTs suchthat the tubes are maximally proximate or near maximally proximate toeach other. In the case of a MWNT, the nested shells are intrinsicallybundled. In the case of numerous MWNTs, bundling is accomplished byplacing the MWNTs in a maximally proximate configuration. In the case ofSWNTs, bundling is accomplished by placing the SWNTs in a maximallyproximate configuration. Similarly, in the case of a mixture of SWNT(s)and MWNT(s), bundling is accomplished by placing these CNTs in amaximally proximate configuration.

SUMMARY OF THE INVENTION

[0044] The present invention provides a composition comprising asingle-walled or multi-walled carbon nanotube, having phase-coherent orphase incoherent superconductivity above about 20 K.

[0045] The present invention provides a composition comprising amulti-walled carbon nanotube, having phase-coherent superconductivityabove about 20 K.

[0046] The present invention provides a composition comprising a bundleof single-walled or multi-walled carbon nanotubes, having phase-coherentor phase incoherent superconductivity above about 20 K.

[0047] The present invention provides a composition comprising a bundleof multi-walled carbon nanotubes, having phase-coherentsuperconductivity above about 20 K.

[0048] The present invention provides a composition comprising a matrixincluding bundles of multi-walled nanotubes, having phase-coherentsuperconductivity above about 20 K.

[0049] the present invention provides a composition comprising a matrixincluding bundles of single-walled nanotubes, having phase-coherentsuperconductivity above about 20 K.

[0050] The present invention provides a composition comprising a matrixincluding bundles of single-walled and multi-walled nanotubes, havingphase-coherent superconductivity above about 20 K.

[0051] The present invention also provides methods of achieving a largepositive magnetoresistance in bundles of superconducting carbonnanotubes above about 20 K.

[0052] The present invention also provides superconducting quantuminterference devices comprising a composition of this invention.

[0053] The present invention also provides magnetic reading headscomprising a composition of this invention.

[0054] The present invention also provides magnetic switch devicescomprising a composition of this invention.

[0055] The present invention also provides magnetic image devicescomprising a composition of this invention.

[0056] The present invention also provides conductive elementscomprising a composition of this invention.

[0057] The present invention also provides two or more electronicelements interconnected by a conductive element comprising a compositionof this invention.

[0058] The present invention also provides a method for formingsuperconducting materials comprising forming a composition includingnanotubes or nanotube bundles of this invention, aligning the nanotubesor bundles and forming the aligned nanotube or bundles into an elongateform.

DESCRIPTION OF THE DRAWINGS

[0059] The invention can be better understood with reference to thefollowing detailed description together with the appended illustrativedrawings in which like elements are numbered the same:

[0060]FIG. 1A depicts the temperature dependence of the remnantmagnetization for multi-walled nanotubes. After [1];

[0061]FIG. 1B depicts the field-cooled susceptibility as a function oftemperature in a field of 0.020 Oe. After [1];

[0062]FIG. 2 depicts the temperature dependence of the conductance for amulti-walled nanotube rope (reproduced from Ref [3]);

[0063]FIG. 3A depicts the Hall coefficient versus temperature for ananotube rope (reproduced from Ref. [3]);

[0064]FIG. 3B depicts the Hall voltage as a function of magnetic fieldmeasured at different temperatures, solid lines are drawn to guide theeye (reproduced from Ref. [3]);

[0065]FIG. 4 depicts the Hall coefficient component for physicallyseparated tubes (PS) and the component for Josephson-coupledsuperconducting tubes (JC);

[0066]FIG. 5A depicts the Hall voltage component for physicallyseparated tubes (PS) at 5 K;

[0067]FIG. 5B depicts the Hall voltage component for Josephson-coupledsuperconducting tubes (JC) at 5 K;

[0068]FIG. 6A depicts the temperature dependence of the four-proberesistance for a single MWNT with d=17 nm (reproduced from Ref [20]);

[0069]FIG. 6B depicts the temperature dependence of the resistance over10-60 K, which is fitted by R(T)=R_(ct)+aT^(P). The fitting parameters:R_(ct)=5.6(5)kΩ, p=−0.65(9), and a=29(4)kΩK^(0.65);

[0070]FIG. 7A depicts the temperature dependence of the resistance for aSWNT (data extracted from Ref. [26]);

[0071]FIG. 7B depicts the temperature dependence of the resistance forthree ultra-thin MoGe wires. The curves are smoothed from the originalplot of Ref. [18];

[0072]FIG. 8 depicts the I-V characteristic observed in a MWNT withd=9.5 nm. The figure is reproduced from Ref. [30];

[0073]FIG. 9 depicts the critical current I_(c)(T) for a SWNT rope (dataextracted from Ref. [38]), solid line represents calculated curve usingEq. 8 and T_(c0)=580 mK;

[0074]FIG. 10A depicts the critical currents i_(c)'s at 300 K for theindividual superconducting layers in a MWNT with d=9.5 nm and in a MWNTwith d=15 nm (data extracted from Ref. [30]);

[0075]FIG. 10B depicts the mean-field critical temperature, I_(c)'s, ofindividual superconducting layers in the MWNTs with d=9.5 nm and 15 nm,respectively, (T_(c0)'s are calculated using Eq. 9 and assumingi_(c)=i_(c1));

[0076]FIG. 11A depicts the temperature dependence of the frequency forthe Raman-active Big mode of a 90 K superconductor YBa₂Cu₃O_(7-y) (dataextracted from Ref. [42]);

[0077]FIG. 11B depicts the difference of the measured frequency and thelinearly fitted curve above T_(c);

[0078]FIG. 12 depicts the temperature dependence of the frequency forthe Raman active G-band of single-walled carbon nanotubes containingdifferent concentrations of the magnetic impurity Ni:Co (curvesreproduced from the original plot of Ref. [41]);

[0079]FIGS. 13A, B & C depict the difference between the measuredfrequency and the linearly fitted curve above the kink temperatures (seetext);

[0080]FIG. 14 depicts the T_(c0) as a function of the magnetic impurity(Ni:Co) concentration in SWNTs;

[0081]FIG. 15A depicts the resistance data as a function of T/T_(c0) forthe smallest diameter SWNT with d=0.42 nm (data extracted from Ref.[46]);

[0082]FIG. 15B depicts the temperature dependence of the resistancebelow 0.5T_(c0) (data are well fitted by R(T)=R_(o)+T_(β) withβ=1.77±0.18;

[0083]FIG. 16 depicts temperature dependence of the resistivity for aSWNT rope (data extracted from Ref. [47]);

[0084]FIG. 17 depicts temperature dependence of the resistance for asingle-walled nanotube with d=1.5 nm (data extracted from Ref. [49]);

[0085]FIG. 18 depicts the calculated T_(c) as a function of the arealcarrier density for InSb wires of the cross sections of 50 nm×10 nm and80 nm×10 nm (curves reproduced from the original plot of Ref [55]);

[0086]FIG. 19 is an illustration of the decrease in resistance with theincrease in the number of the conducting layers in the MWNTs, where R isresistance;

[0087]FIG. 20 is an illustration of the effect the SWNT bundles have onresistance, where diameters of the SWNTs in the bundle are notnecessarily identical and R is resistance;

[0088]FIG. 21 is an illustration of the effect MWNT bundle configurationhas on resistance, where the diameters and the numbers of the adjacentsuperconducting layers of the MWNTs in the bundle are not necessarilyidentical and R is resistance; and

[0089]FIG. 22 is an illustration of superconducting quantum interferencedevices (SQUIDs) constructing from two phase coherent superconductingMWNTs or from two phase coherent superconducting bundles.

DETAILED DESCRIPTION OF THE INVENTION

[0090] The inventor has found that certain chiral carbon nanotubesdisplay superconducting properties at or above room temperature.Although the inventor has found that any carbon nanotubes can be madeinto superconductors through judicious doping, chiral nanotubes havingmetallic chiralities are preferred. Carbon nanotubes can be electrondoped or hole doped. Doping can be achieved via gate charging,interfacing with a metal having a different work function from the tube,or a chemical or a physical dopant selected from the group consisting ofoxidants, reductants, dopants resulting from atom or ion implantation,dopants from charged particle bombardment or the like. The preferreddoping method is the gate charging where doping does not introducedisorder. Metallic chirality carbon nanotubes are capable ofsuperconducting with even minor amount of doping and can superconduct atany doping level in excess of a threshold dopant level. For example,SWNTs with metallic chiralities and a diameter of d=1.5 nm exhibit phaseincoherent superconductivity above 600 K when the doping lever is about0.3% per carbon. The preferred doping level corresponds to a Fermi levelsuch that the first metallic subband is nearly occupied. Therelationship between the Fermi energy E_(F) and carrier concentrationper carbon n is given by n=0.0204|E_(F)|/d, where the diameter d is inunit of nanometer and the Fermi energy E_(F) is in unit of eV. When theconcentration of doped holes or electrons is close to 0.019/d² percarbon, the first subband is completely occupied. The preferred diameterof the tube for maximizing superconducting transition temperature isabout 1 nm.

[0091] The inventor has also found a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity whereby nested metallic chirality layers in MWNT areformed whereby the resistance can be tuned based on the number of nestedmetallic chirality layers—an increase in layers decreases resistivity.The most phase coherent superconductivity occurs when all the nestedlayers have metallic chiralities and the intra-nested tube distance isas small as possible. This is due to an effective increase in the numberof the transverse channels via the Josephson coupling of adjacentsuperconducting layers. The resistance decreases exponentially withincreasing nested superconducting layers. The zero resistance or phasecoherent state can be approached in a single MWNT that consists ofnested superconducting layers that meet or surpass the minimum number ofnested layers to achieve high temperature superconductivity.

[0092] The inventor has also found a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity. SWNTs are bundled by putting several metallicchirality SWNTs in parallel and packed adjacent to each other. Thisresults in a much lower resistance than the sum of the individual tubes.The diameters of the SWNTs in the bundle are not necessarily identical.The preferred embodiment occurs where the inter-tube distance is asclose as possible. The Josephson coupling among the tubes can suppressthe QPS and lower the resistance exponentially.

[0093] The inventor has also found a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity whereby several phase-incoherent superconducting MWNTsare put in parallel and packaged in an adjacent configuration, theresulting bundle has lower resistance than the sum of the individualtubes. The diameters and the numbers of the adjacent superconductinglayers of the MWNTs are independent and need not be identical. Thepreferred embodiment occurs where the inter-tube distance is as close aspossible. The Josephson coupling among the tubes can suppress the QPSthereby exponentially lowering the resistance and approaching the zeroresistance state.

[0094] The inventor has also found a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity whereby several phase-incoherent superconducting MWNTsand SWNTs are put in parallel and packaged in an adjacent configuration,the resulting bundle has lower resistance than the sum of the individualtubes. The preferred embodiment occurs where the inter-tube distance isas close as possible.

[0095] The inventor has also found a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity by combining the embodiments above whereby a bundle ofMWNTs and SWNTs are combined.

[0096] As discussed above, phase coherent superconducting materials canbe constructed by forming aggregates of superconducting carbon nanotubes(SCNTs) where the nanotubes are in proximity to each other in an alignedorientation, preferably in maximal proximity. The condition where aconsiderable portion of lengths of two or more nanotubes are alignedalong an axis and are in close proximity, preferably maximal proximity,and are wrapped into bundles with a spiral winding—or otherwise—tomaintain the alignment and intimate proximity or to control thealignment and proximity or to vary the alignment and proximity shouldprove to secure electronic properties of the collection of SCNTs. Apreferred implementation is the securing in a maximally proximate mannerof optimally doped superconducting MWNTs-optimized in terms of thedoping and chirality.

[0097] The inventor has also found that there is a very large positivemagnetoresistance (MR) effect in bundles of superconducting carbonnanotubes. The bundles are preferably closely packed, as discussedabove. In order to have a substantial low field MR effect, the size ofsuperconducting bundles must exceed a critical value. The critical valueof the size is inversely proportional to the square root of the magneticfield used in the application. Any existing device in which materialswith this type MR effect are used can be converted into new deviceswhere the old materials are replaced by bundles of superconductingcarbon nanotubes of this invention. The new devices will have improvedperformances.

[0098] The inventor has also found that very sensitive magnetic readingheads can be constructed from bundles of superconducting carbonnanotubes, which have a large MR effect. A magnetic field created from aferromagnetic domain in a tape or a diskette changes the resistance ofthe reading head comprising a bundle of superconducting carbonnanotubes. Because of the very large MR effect, any small change in themagnetic field can lead to a large change in the resistance of the head.Therefore, the sensitivity of the magnetic reading head will be veryhigh. Moreover, the size of the head can be very small (on the order of50 nm), so the spatial resolution is also very high. The performance ofthis type of magnetic reading heads should be superior to any one in themarket.

[0099] The inventor has also found that because of the superiorsensitivity and spatial resolution, the magnetic reading head can beused as a sensor of high resolution magnetic imaging spectroscopy. Withthis spectroscopy, the magnetic domain patterns in magnetic materialscan be clearly seen. This spectroscopy will be a powerful device todiagnose magnetic memory cards, magnetic taps and diskettes, currentdistributions of chips, and so on.

[0100] The inventor has also found that very sensitive magnetic switchdevices can be constructed from bundles of superconducting carbonnanotubes, which have a large MR effect. A small change of the magneticfields near a bundle of superconducting carbon nanotubes will lead to alarge change in the resistance of the bundle. The magnetic field can beproduced by a current or a permanent magnet. Changing the current or thedistance between the permanent magnet and the bundle gives rise to thechange in the magnetic field near the bundle and therefore to the changeof the resistance in the bundle. The change of the resistance in thebundle serves as an input signal to trigger an electrical switch to openor close.

[0101] The inventor has also found that superconducting quantuminterference devices (SQUIDs) can be constructed from phase-coherentsuperconducting nanotubes. A single phase-coherent MWNT is preferred forthis type of device. This device can probe an extremely weak magneticfield, operate at room temperature, and have a superior spatialresolution. This superior performance of the device enables it to mapthe magnetic field distribution in the body of our human being, which isclosely related to our health. Therefore it can be used to diagnose oursymptoms, leading to an important application in medicine. The roomtemperature SQUIDs should have much broader applications thanconventional low temperature SQUIDs.

[0102] The inventor has also found that superconducting materials can beprepared from multi-layered graphite or graphene sheets that areappropriately doped. Preferably, the graphite or graphene materialscomprise graphite sheets that have the same structure. Such structures,when appropriately doped, will superconduct, coherently or incoherently,at temperatures above 100 K, preferably above about 200 K andparticularly at or above about 300 K.

[0103] Transport and Magnetic Properties in Multi-wall Carbon NanotubeRopes: Evidence for Superconductivity above Room Temperature

[0104] Here, the inventor provides detailed data analyses on theexisting data for multi-walled nanotube ropes. In terms of thecoexistence of physically separated (PS) tubes and Josephson-coupled(JC) superconducting tubes with superconductivity above roomtemperature, the inventor can consistently explain the temperaturedependencies of the Hall coefficient, the magnetoresistance effect, theremnant magnetization, the diamagnetic susceptibility, and theconductance, as well as the field dependence of the Hall voltage. Theinventor also interprets the observed paramagnetic signal and unusualfield dependence of the magnetization at 300 K as arising from theparamagnetic Meissner effect in a multiply connected superconductingnetwork.

[0105] The inventor first discusses the temperature dependencies of theremnant magnetization M_(r) and the diamagnetic susceptibility for hismult-walled nanotube ropes. Plotted in FIG. 1 are the experimentalresults which are reproduced from Ref. 1. It is apparent that thetemperature dependence of the M_(r) (FIG. 1A) is similar to that of thediamagnetic susceptibility (FIG. 1B) except for the opposite signs. Thisbehavior is expected for a superconductor. The M_(r) was also observedby Tsebro et al. up to 300 K [2]. However, the observation of the M_(r)alone does not give evidence for superconductivity since the M_(r) couldbe caused by ferromagnetic impurities and/or ballistic transport.

[0106] The inventor can rule out the existence of ferromagneticimpurities. If there were ferromagnetic impurities, the totalsusceptibility would tend to turn up below 120 K where the M_(r)increases suddenly. This is because the paramagnetic susceptibilitycontributed from the ferromagnetic impurities would increase below 120K. In contrast, the susceptibility suddenly turns down rather than turnsup below 120 K (FIG. 1B). This provides strong evidence that theobserved M_(r) in the nanotubes has nothing to do with the presence offerromagnetic impurities.

[0107]FIG. 2 shows temperature dependence of the conductance for amulti-walled nanotube rope, which is reproduced from Ref. 3. Theinventor has checked that the temperature dependence of the conductancein his nanotube ropes is nearly the same as that shown in FIG. 2. It isapparent that the conductance for the MWNT sample tends to increasebelow 120 K at which both remnant magnetization and the field-cooleddiamagnetic signal suddenly increase. This suggests that the magneticproperties are closely related to the electrical transport of thenanotubes.

[0108] Alternatively, the increase of the conductance below 120 K couldbe due to the increase in the ballistic conduction channels (perfectconductivity). However, this scenario cannot consistently account forthe observed increase of the field-cooled diamagnetic signal below 120 Ksince perfect conductors cannot expel the magnetic flux in thefield-cooled condition.

[0109] In FIG. 3, the inventor shows the temperature dependence of theHall coefficient (FIG. 3A) and the field dependence of the Hall voltage(FIG. 3B) for a multi-walled nanotube rope. The figures are reproducedfrom Ref. 3. It is striking that the Hall coefficient increases rapidlybelow about 120 K at which all three quantities in FIG. 1 and FIG. 2increase suddenly. The fact that such a strong temperature dependencebelow 120 K was not seen in physically separated tubes [4] suggests thatthis is not an intrinsic property of a single tube, but associated withthe coupling of the tubes. Below the inventor will interpret these datain a consistent way by considering the coexistence of physicallyseparated (PS) tubes and Josephson-coupled (JC) superconducting tubeswith superconductivity above room temperature.

[0110] It is well known that the carbon nanotubes have two types ofelectronic structure depending on the chirality [5, 6], which is indexedby a chiral vector (n,m): n−m=3N+ν, where N, n, m are the integers, andν=0, +i. The tubes with ν=0 are metallic while the tubes with ν=+1 aresemiconductive. The multi-walled nanotubes consist of at least twoconcentric shells which could have different chiralities. Presumably,each shell should exhibit phase incoherent superconductivity when it issufficiently doped. If there are sufficient adjacent superconductingshells that are Josephson coupled, a single MWNT could become a phasecoherent non-dissipative superconductor. If phase incoherentsuperconducting tubes are closely packed into a bundle, the bundle couldbecome a phase coherent superconductor via Josephson coupling. It isalso possible that some tubes are not superconducting due toinsufficient doping.

[0111] The inventor could classify the tubes in a rope into physicallyseparated (PS) tubes and Josephson-coupled (JC) superconducting tubeswith superconductivity above room temperature. Since the properties forphysically coupled nonsuperconducting tubes should have no differencesfrom that for physically separated nonsuperconducting tubes, Theinventor considers all nonsuperconducting tubes as physically separatedtubes.

[0112] The Hall coefficient for physically separated tubes should bepositive, as reported in Ref. [4]. The Hall coefficient for a singlenon-dissipative superconducting MWNT should be zero because no vorticescould be trapped into the single tube whose dimension should be muchsmaller than the inter-vortex distance. The physically separatednonsuperconducting and phase-incoherent dissipative superconductingtubes should have a positive Hall coefficient similar to that in thenormal state. On the other hand, vortices can be trapped intoJosephson-coupled superconducting tubes, leading to a vortex-liquidstate above a characteristic field that depends on the Josephsoncoupling strength. As seen in both cuprates and MgB₂ [7, 8], thelow-field Hall coefficient RH in the vortex-liquid state is negativebelow T_(c), reaching a minimum at T_(k), and then increasing towardszero with further decreasing temperature. Below the characteristictemperature T_(k), vortices start to be pinned so that magnitudes of theHall conductivity, longitudinal conductivity, the critical current(remnant magnetization), and diamagnetic susceptibility increasesimultaneously. This can naturally explain why the conductance, thediamagnetic susceptibility, the remnant magnetization, and the Hallcoefficient simultaneously increase below about 120 K, as seen from FIG.1, FIG. 2 and FIG. 3A.

[0113] The inventor can decompose the total Hall coefficient into twocomponents: one is for Josephson-coupled superconducting tubes (JC) andanother for physically separated tubes (PS). The PS component isproportional to the measured Hall coefficient for physically separatedtubes [4] with the constraint that, at zero temperature, the magnitudeof the PS component is equal to the total Hall coefficient. The JCcomponent is obtained by subtracting the total Hall coefficient from thePS component. FIG. 4 shows both PS (dashed line) and JC (solid line)components. It is apparent that the JC component has a local minimum atT_(k)=120 K. The negative value of the JC component remains up to 200 K.This suggests that the superconducting transition temperature is farabove 200 K.

[0114] Similarly, as seen in cuprates and MgB₂ [7, 8, 9], the Hallvoltage V_(H) in the vortex-liquid state is negative, passing through aminimum at B_(k), and then increasing towards the normal-state valuewith further increasing temperature. Below B_(k), V_(H) tends to zero.Interestingly, both B_(o) and B_(k) can be independently obtained fromthe field dependence of the longitudinal resistivity, as described inRef. 9.

[0115] The inventor can also decompose the total Hall voltage into twocomponents: one for Josephson-coupled superconducting tubes (JC) andanother for physically separated tubes (PS). Plotted in FIG. 5A is thePS component at 5 K, which is proportional to the measured Hall voltagefor physically separated tubes [4] and matches with the low field datashown in FIG. 3B. FIG. 5B shows the JC component at 5 K, which isobtained by subtracting the total Hall voltage from the PS component.The decomposition was performed after the data in FIG. 3B were smoothed.The inventor can see that the field dependence of the JC component isquite similar to that for cuprates and MgB₂ [7, 8, 9] except that B_(o)in the MWNTs is rather small, which may be due to a weak pinningpotential. FIG. 5B also indicates that the magnitude of B_(k) is largerthan 5 T, in agreement with the longitudinal magnetoresistance data (seebelow).

[0116] The longitudinal magnetoresistance at 300 K mainly arises fromthe Josephson-coupled superconducting tubes since the contribution fromthe physically separated tubes is negligible [4]. From themagnetoresistance data at 300 K [3] and the criterion for determiningB_(k)[9], the inventor finds that B_(k)≈3.0 T at 300 K. Using therelation B_(k)(T)=B_(k)(0)(1−T/T _(c))^(1.5) [9], T_(c)=650 K [1], andB_(k)(300 K)=3.0 T, one has B_(k)(5 K)=7.5 T. This could explain why onehas not seen the local minimum in V_(H) below 5 T. It is highlydesirable to perform the Hall effect experiment up to 15 T to see thecrossover field B_(k).

[0117] Within this two component model, the inventor can also explainthe unusual magnetoresistance (MR) effect below 150 K. Because thephysically separated tubes produce a negative MR effect at lowtemperatures while the Josephson-coupled superconducting tubes generatea positive MR effect, the opposite contributions from the two componentscan lead to a local minimum at certain magnetic field. This is indeedthe case (see FIG. 1 of Ref. 3). At high temperatures, the negative MReffect contributed from the physically separated tubes becomes weak sothat the positive MR effect is mainly contributed from theJosephson-coupled superconducting tubes, in agreement with theexperimental results [1, 3].

[0118] There are more experimental results that support the thesis ofroom temperature superconductivity in multi-walled nanotubes. Theobservation of the paramagnetic signal at 300 K below H=2 kOe [10] isremarkable, which can be explained as arising from the presence offerromagnetic impurities or from the paramagnetic Meissner effect belowthe superconducting transition temperature, as observed in ceramiccuprate superconductors [11] and in multijunction loops of conventionalsuperconductors [12]. For H=4000e, the temperature dependence of thesusceptibility for the nanotube sample (see FIG. 8 of Ref. 10) issimilar to that for a ceramic cuprate superconductor in a low field (seeFIG. 10a of Ref. 11). The M (H) curve below H=10 kOe (see FIG. 7 of Ref.10) can be compatible with the presence of ferromagnetic impurities.However, such ferromagnetic impurities should be detectable in thehigh-field magnetization curve by an intercept in the extrapolation forH→0. The intercept was found to be nearly zero at 300 K in the samplesof Ref. 10. In the inventor's samples prepared from graphite rods withthe same purity (99.9995%), the intercepts are negligible in the wholetemperature range of 250 K to 400 K. For less pure C₆₀ and graphitesamples, the contamination of ferromagnetic impurities is clearly seenfrom the M (H) curve in the high-field range [10]. The clear“ferromagnetic” signal observed only in the low field range [10] issimilar to the case in granular superconductors [11]. The“ferromagnetic” signal may be caused by a “ferromagnetic” ordering ofelementary long-thin current loops [13]. The critical magnetic fieldbelow which the “ferromagnetic” state is stable should depend on thenumber of filaments per current loop. The large critical field of about10 kOe in the samples of Ref. 10 suggests that a current loop maycorrespond to a bundle consisting of a large number of tubes.

[0119] Quasi-one-dimensional Superconductivity above 300 K and QuantumPhase Slips in Individual Carbon Nanotubes

[0120] Here the inventor extensively analyzes a great amount of theexisting data for electrical transport, the Altshuler Aronov Spivak andAharonov Bohm effects, as well as the tunneling spectra of individualcarbon nanotubes. The data can be explained by theories of the quantumphase slips in quasi-one-dimensional superconductors. The existing dataconsistently suggest that the mean-field superconducting transitiontemperature T_(c0) in both single-walled and multi-walled carbonnanotubes could be higher than 600 K. Remarkably, the QPS theories cannaturally explain why the resistances in the closely packed nanotubebundles or in the individual multi-walled nanotubes with large diametersapproach zero at room temperature, while a single tube with a smalldiameter has a non-zero resistance.

[0121] It is known that superconducting fluctuations in one-dimensional(1 D) superconductors play an essential role in the resistivetransition. Slightly below superconducting transition temperatureT_(c0), 1D superconductors have a finite resistance due to thermallyactivated phase slips (TAPS) [14]. A number of experiments have alsodemonstrated a large resistance well below T_(c0) in thinsuperconducting wires [15, 16, 17, 18]. Further, a crossover to aninsulating state has been observed in ultra-thin PbIn wires withdiameters of the order of 10 nm [15, 17] as well as in ultra-thin wiresof MoGe [18].

[0122] Theories based on the quantum phase slips can explain the finiteresistance in 1D superconductors [16, 19]. Essentially, the phase slipsat low temperatures are related to the macroscopic quantum tunneling(MQT), which allows the phase of the superconducting order parameter tofluctuate between zero and 2π at some points along the wire, resultingin voltage pulses. The QPS tunneling rate is proportional to exp(−S_(QPS)), where S_(QPS) in clean superconductors is very close to thenumber of transverse channels N_(ch) in the limit of weak damping (seebelow). If the number of the transverse channels N_(ch) is small, theQPS tunneling rate is not negligible, leading to a non-zero resistanceat low temperatures. For a single-walled nanotube (SWNT), N_(ch)=2,implying a large QPS tunneling rate and thus a large resistance even ifit is a superconductor. For MWNTs with several superconducting layersadjacent to each other, the number of the transverse channels willincrease substantially, resulting in the suppression of the QPS. If twosuperconducting tubes are closely packed together to effectivelyincrease the number of the channels, one would find a small resistanceat room temperature if the constituent tubes have a mean-field T_(c0)well above room temperature. This can naturally explain why a singleMWNT with a diameter d of about 17 nm has a finite on-tube resistance atroom temperature [20, 21] while a bundle consisting of two tubes has anegligible on-tube resistance [22].

[0123] There are thermally activated phase slips and quantum phase slipsin a thin superconducting wire. In a theory developed by Langer,Ambegaokar, McCumber and Halperin [14], such phase slips occur viathermal activation. The resistance due to the TAPS is given by [23]$\begin{matrix}{R_{T\quad A} = {( \frac{h}{4e^{2}} )( \frac{\hslash \quad \Omega}{k_{B}T} ){\exp ( {- \frac{\Delta \quad F_{0}}{k_{B}T}} )}}} & (1)\end{matrix}$

[0124] where the attempt frequency Ω is given by [14] $\begin{matrix}{\Omega = {( \frac{3^{\frac{1}{2}}}{2\quad \pi^{\frac{3}{2}}} )( \frac{L}{\xi} )( \frac{\Delta \quad F_{0}}{k_{B}T} )^{\frac{1}{2}}( \frac{1}{\tau} )}} & (2)\end{matrix}$

[0125] where L is the length of the wire, 4 is the coherence length, andh/τ=(8/π)k_(B)(T_(c)−Y). The barrier energy ΔF_(o) is $\begin{matrix}{{\Delta \quad F_{0}} = {( \frac{2^{\frac{7}{2}}}{3} )( \frac{H_{c}^{2}}{8\quad \pi} )A\quad \xi}} & (3)\end{matrix}$

[0126] where H_(c) ²/8π is the condensation energy and A is thecross-section area of the wire. The condensation energy is equal to N(0)Δ²/2 within the BCS theory, where N(0) is the average density ofstates near the Fermi level over the energy scale of the superconductinggap Δ. For a metallic SWNT with N_(Ch)=2, N (0)Δ=4/(3πa_(c-c)y_(o))(Ref. 24),

ν_(F)=1.5a_(c-c)γ_(o) (Ref 25), where γ_(o) is the hopping integral, ris the radius of the tube, and _(c-c) is the bonding length. Using ξ=

ν_(F)/πΔ and the above relations, one can readily show that ΔF_(o)τ/

=0.13 N_(ch) and ΔF_(o)≅0.19 N_(ch). For MWNTs with N_(m) metalliclayers, ΔF_(o)τ

=0.26 N_(m) and ΔF_(o)/Δ=0.38 N_(m).

[0127] It was shown that the TAPS is significant only at temperaturesvery close to and below T_(c0) [14]. At lower temperatures, the finiteresistance is caused by MQT and is given by [16], $\begin{matrix}{R_{MQT} = {{\beta_{1}( \frac{h}{4e^{2}} )}( \frac{L}{\xi} )( \frac{\beta_{2}\Delta \quad F_{0}\tau}{\hslash} )^{\frac{1}{2}}{\exp ( {{- \beta_{2}}\Delta \quad F_{0}{\tau/\hslash}} )}}} & (4)\end{matrix}$

[0128] where β₁ and β₂ are constants, depending on the damping strength.When the damping increases, β₂ decreases. Substituting ΔR_(o)τ/

=0.26N_(m) into Eq. 4, the inventor finds that $\begin{matrix}{R_{MQT} = {{\beta_{1}( \frac{h}{4e^{2}} )}( \frac{L}{\xi} )( {0.26\beta_{2}N_{m}} )^{\frac{1}{2}}{\exp ( {{- 0.26}\beta_{2}N_{m}} )}}} & (5)\end{matrix}$

[0129] From Eq. 5, one can see that S_(QPS)=2N_(m) in the limit of weakdamping where β₂=7.2 (Ref. 16). For a stronger damping, P2 is reduced sothat S_(QPS)<2N_(m). Moreover, in the dirty limit, S_(QPS) will befurther reduced [19] such that S_(QPS)<<2N_(m). For a SWNT, N_(m)=1 sothat a large QPS and a nonzero resistance is expected below themean-field superconducting transition temperature. If severalsuperconducting SWNTs are closely packed to ensure an increase in thenumber of channels, the QPS would be substantially reduced. This canexplain why the resistance is finite at room temperature for a singleSWNT [26, 27] while the resistance at room temperature is very small fora bundle consisting of two strongly coupled SWNTs [21]. For a MWNT withd=40 nm, there is a total of 27 metallic layers, that is, N_(m)=27 (Ref.28). This implies that the QPS in this single MWNT should be stronglysuppressed according to Eq. 5. Indeed, this MWNT has nearly zeroresistance at room temperature over a length of 4 μm (Ref. 28).

[0130] A more rigorous approach to the QPS in quasi-1D superconductors[19] suggests that S_(QPS) depends not only on the quantity ΔF_(o)τ/

but also on the normal-state conductivity σ(S_(QPS)∝σ^(2/3)) Therefore,one can very effectively suppress the QPS and the resistance belowT_(c0) by reducing the normal-state resistivity. It was shown that theelectron backscattering from single impurity with long range potentialis nearly absent in metallic SWNTs while this backscattering becomessignificant for doped semiconducting SWNTs [29]. This implies that theQPS in doped metallic SWNTs will be significantly smaller than that indoped semiconducting SWNTs if both systems become superconducting bydoping.

[0131] Now the inventor discusses the temperature dependence of theresistance observed in nanotubes. FIG. 6A shows the temperaturedependence of the four-probe resistance for a single MWNT with d=17 nm,which is reproduced from Ref. 20. It is remarkable that the resistanceincreases with decreasing temperature, but saturates at lowtemperatures. This unusual temperature dependence is very difficult tobe explained consistently in terms of the conventional theory oftransport [20]. However, a theory based on the QPS in 1 Dsuperconductors can naturally explain this unusual behavior. It wasshown that [19], the resistance R˜T^(2Υ−3) for k_(B)T>>Φ_(o)I/c, and Rbecomes independent of temperature and is proportional to I^(2μ−3) fork_(B)T<<Φ_(o)I/c, where Φ_(o) is the quantum flux, c is the speed oflight, and I is the current. When μ<1.5, R increases with decreasingtemperature (semiconducting behavior), while μ>1.5, R decreases withdecreasing temperature (metallic behavior). Only if the QPS are stronglysuppressed, zero or negligible resistance state can be realized belowT_(c0).

[0132] Based on the QPS theory, the inventor can readily show that, forΦ_(o)I/ck_(B)<<T<<T_(c), the four-probe resistance R(T) is

R(T)=R _(ct) +aT _(P)  (6)

[0133] where R_(ct) is the tunneling resistance and p=2μ−3. Thetunneling resistance is given by R_(ct)=R_(Q)/tN_(ch), where t is thetransmission coefficient (t<1) and R_(Q)=h/2e²=12.9 kΩ is the resistancequantum.

[0134] In FIG. 6B, the inventor fit the resistance of the MWNT by Eq. 6.The best fit gives R_(ct)=5.6(5) kΩ, p=−0.65(9), and α=29(4) kΩK^(0.65). The value of R_(ct) suggests that the intrinsic saturationresistance of the tube is 9.7 kΩ.

[0135] From the value of R_(ct) for the MWNT, the inventor can estimatethe transmission coefficient t. As discussed below, the high biastransport measurements in MWNTs [30] suggest that there is a total of 14conducting layers in a MWNT with d=14 nm, and that the number of theconducting layers is nearly proportional to d. Then, the MWNT with d=17nm should have about 17 conducting layers. Moreover, the beautifulexperiment reported by de Pablo et al. [28] indicates that eachconducting layer contributes 1 transverse channel to electricaltransport. Therefore, one expects N_(ch)=17 in this MWNT, leading tot=0.135. This suggests that the tunneling is far from being ideal, whichmay arise from non-Ohmic contacts. It should be mentioned that eachlayer should contribute 2 channels if there were no interlayer coupling.However, it has been shown that the interlayer coupling cansignificantly modify the electronic states near the Fermi level, leadingto the modulation in the number of channels between 1 and 3 for eachlayer (the average number of channels over an energy scale of 0.1 eVremains 2 for each layer) [31, 32].

[0136] In FIG. 7A, the inventor plots the temperature dependence of theresistance for a single SWNT. The data are extracted from Ref. 26. It isinteresting that the temperature dependence of the resistance in thesingle-walled nanotube is similar to that found for ultra-thin wires ofMoGe superconductors [18], which is reproduced in FIG. 7B. Thecharacteristic temperature T* corresponding to the local resistanceminimum depends on the resistance in the normal state. It appears thatT* decreases with decreasing the resistance. The resistance at lowtemperatures could be smaller or larger than that in the normal state.By comparing FIG. 7A and FIG. 7B, one might infer that the mean-fieldT_(c0) of this nanotube is well above 270 K.

[0137] From the single-particle tunneling spectrum obtained through twohigh-resistance contacts (see FIG. 6b of Ref. 27), the inventor canclearly see a pseudo-gap feature appears at an energy of about 220 meV.The pseudo-gap feature should be related to the superconducting gap.Considering the broadening of the gap feature due to large QPS and thedouble tunneling junctions in series, The inventor estimates thesuperconducting gap A to be about 100 meV. The scanning tunnellingmicroscopy and spectroscopy [33] on individual single-walled nanotubesalso show the pseudo-gap features with Δ=100 meV in doped metallic SWNTs(E_(F) is about 0.2 eV below the top of the valence band). Usingk_(B)T_(c0)=Δ/1.76, one finds T_(c0)=660 K. It is interesting to notethat the pseudo-gap feature could be explained by Luttinger-liquidtheory [34, 35] assuming that the Luttinger parameter is far below thefree fermionic value of 1. The fact that the pseudo-gap feature is seenonly in doped metallic chirality tubes [33] but not in undoped armchairmetallic chirality tubes [36] may rule out the Luttinger-liquidexplanation since Luttinger-liquid behavior remains essentiallyunchanged with doping [35].

[0138] Now the inventor explains one of the most remarkable featuresobserved in the carbon nanotubes. At large biases, the current saturatesat 19-23 μA in SWNTs [27]. The current saturation has been explained asdue to the backscattering of the zone-boundary optical phonons [27].However, the deduced mean free path for the phonon backscattering is oneorder of magnitude smaller than the expected one from the tight-bindingapproximation [27]. Further, the I-V characteristic observed in SWNTs istemperature independent (Ref. 27) while the calculated I-Vcharacteristic within this mechanism strongly depends on temperatureespecially in the low-bias range [37].

[0139] Alternatively, the inventor can explain the I-V characteristicsof both SWNTs and MWNTs [27, 30] in terms of quasi-1D superconductivity.Essentially, the I-V characteristics of both SWNTs and MWNTs [27, 30]are similar to that observed in ultra-thin PbIn superconducting wires(see FIG. 8 of Ref. 17). FIG. 8 shows the I-V characteristic observed ina MWNT with d=9.5 nm. The figure is reproduced from Ref. 30. When theapplied current is below I_(c1) the QPS are negligible so that theintrinsic on-tube resistance is much smaller than the normal-stateresistance, and V depends on I quasi-linearly. The slope dV/dI is equalto the sum of the on-tube resistance and the contact resistance. Whenthe applied current increases slightly above I_(c1), the on-tuberesistance rises rapidly towards the normal-state value due to largeQPS, leading to large dissipation that would burn the tube. If the tubeis not burned, the current tends to be saturated before the tube iscompletely driven into the normal state. The saturation current is closeto the mean-field critical current I_(c) in the absence of defects.Since the phase slips occur initially near normal regions located arounddefects in the sample, one expects that I_(c1) should strongly depend onthe density of defects and thus on the normal-state resistivity. FromFIG. 8, one can see that I_(c1)<0.75I_(c).

[0140] According to the BCS theory, the mean-field critical current inthe clean limit is given by $\begin{matrix}{{I_{c}(T)} = {{n_{s}(T)}{A\lbrack \frac{\Delta (T)}{\hslash \quad k_{F}} \rbrack}}} & (7)\end{matrix}$

[0141] The superfluid density n_(s)(T)=nλ²(0)/λ²(T), and thenormal-state carrier density n=2N(0)E_(F)=2N(0)

ν_(F)k_(F)=4k_(F)/Aπ. Here one has used the relations:N(0)A=4/(3πa_(c-c)γ_(o)), and

ν_(F)=15a_(c-c)γ_(o), as well as E=

ν_(F)|k|. Substituting the above relations into Eq. 7 yields$\begin{matrix}{{I_{c}(T)} = {7.04{{{N_{m}( \frac{k_{B}T_{c0}}{e\quad R_{Q}} )}\lbrack \frac{\lambda^{2}(0)}{\lambda^{2}(T)} \rbrack}\lbrack \frac{\Delta (T)}{\Delta (0)} \rbrack}}} & (8)\end{matrix}$

[0142] with I_(c)(0)=7.04N_(m)k_(B)T_(c0)/eR_(Q). Here λ²(0)/λ²(T)follows the BCS prediction, and Δ(T)=Δ(0) tan h⁻¹[1.6(T_(c0)/T−1)_(1/2)], which is very close to that predicted by theBCS theory. The critical current i_(c) per superconducting layer is thengiven by $\begin{matrix}{{i_{c}(T)} = {7.04{{{N_{m}( \frac{k_{B}T_{c0}}{e\quad R_{Q}} )}\lbrack \frac{\lambda^{2}(0)}{\lambda^{2}(T)} \rbrack}\lbrack \frac{\Delta (T)}{\Delta (0)} \rbrack}}} & (8)\end{matrix}$

[0143] For a SWNT rope, the resistance starts to drop below about 550 mKand reaches a value R_(r)=74 Ω at low temperatures [38]. The data areconsistent with quasi-1D superconductivity with T_(c0)=550 mK andN_(m)=R_(Q)/2R_(r)=87 (Ref 38). Substituting these numbers into theexpression: I_(c)(0)=7.04 N_(m)k_(B)T_(c0)/eR_(Q), one obtainsI_(c)(0)=2.25 μA, in excellent agreement with the measured I_(c)(0)=2.41μA, as seen from FIG. 9. The solid line in FIG. 4 is the calculatedcurve using Eq. 8 and T_(c0)=580 mK. It is striking that the data are inquantitative agreement with theory. It should be mentioned that very lowsuperconductivity in the SWNT rope may be due to the fact that the tubesare very lightly doped. The very high normal-state resistance (830kΩ/μm) per tube [38] suggests that the Fermi level must be very close tothe top of the valence band where the Fermi velocity must besignificantly reduced due to the opening of a small gap in non-armchairmetallic tubes.

[0144] In FIG. 10A, the inventor shows the critical currents i_(c1)'s at300 K for individual superconducting layers in a MWNT with d=9.5 nm andin a MWNT with d=15 nm. The data are extracted from Ref. 30. The layernumber starts from 0 that corresponds to the outermost superconductinglayer. For d=9.5 nm the i_(c) tends to decrease with decreasing thediameter of the layer, while for d=15 nm the tendency is just opposite.Plotted in FIG. 10B is the mean-field critical temperature T_(c0)'s ofindividual superconducting layers in the MWNTs, which are calculatedusing Eq. 9 and assuming i_(c)=i_(c1). It is clear that the calculatedT_(c0)'s are underestimated because i_(c) is always larger than i_(c1),as seen in FIG. 8. One can see that T_(c0) varies from 430 K to 610 K,in good agreement with the independent resistance data [10]. The broadvariation in T_(c0) suggests that T_(c0) depends on doping and thediameters of tubes.

[0145] Now the inventor turns to discuss the Aharonov Bohm (AB) effect,which has been observed in MWNTs when the magnetic field is appliedalong the tube-axis direction [39, 20]. The magnetoresistancemeasurements showed pronounced resistance oscillations as a function ofmagnetic flux. The oscillation period was found to be about Φ_(o)(=hc/2e) if one assumed that only the outermost layer is involved inconduction [39, 20]. The result could be consistent with the AltshulerAronov Spivak (AAS) effect, which arises from quantum interference oftwo counter-propagating closed diffusive electron trajectories. On theother hand, a period of 2Φ_(o) should have been observed if the phasecoherence length of single particles is reasonably larger than πd (theAB effect for the single particle density of states [40]). If the phasecoherence length Lφ deduced from experiment (e.g., Lφ˜300 nm>>πd in oneof the MWNTs [39]) were related to that for single particles, one wouldhave observed the AB effect. However, such an effect has never beenobserved [39, 20]. Therefore, this contradiction cannot be resolved ifthe conduction carriers were single particles.

[0146] The inventor can resolve the above discrepancy if the inventorassumes that the conduction carriers are Cooper pairs in the limit ofweak localization (WL). It was argued that the uncertainty in the phaseof Cooper pairs due to the large QPS could lead to weak localization ofthe Cooper pairs [18]. In many situations, a Cooper pair can beequivalent to a particle with a charge of 8. Therefore, the WL theoryfor single particles should be applicable for Cooper pairs uponreplacing e with 2e. With this simplification, one can readily find thatthe magnetic-flux period of the AAS effect for the Cooper pairs isΦ_(o)/2, and that the AB effect for the single particle density ofstates should be absent if the phase coherence length for singleparticles is less than πd.

[0147] In fact, the assumption that only the outermost layer isconducting [20, 39] is not justified. As the inventor discussed above,14 and 27 layers are involved in conduction in MWNTs with d=14 nm and 40nm, respectively. Further, the resistance at 1.3 K for a MWNT with d=13nm is 2.45 kΩ (Ref. 39). The value of the resistance suggests that thereare at least 6 transverse channels and 6 conducting layers are involvedin conduction. The average magnetic flux sensed by the carriers in allthe conducting layers should be Bπ (r_(out) ²+r_(in) ²)/2, wherer_(out), and r_(in) are the radii of the outermost and innermostconducting layers, respectively, and B is the magnetic field. One cancalculate r_(in) using the relation r_(in)=r_(out)−0.34 (N_(m)−1) nm.For the MWNT with d=17 nm, N_(m)=17 (see above), leading to r_(in)=3.06μm. From the measured magnetic-field period of 8.2 Tin the MWNT [20],one finds that the magnetic-flux period is 0.51 Φ_(o), in quantitativeagreement with the thesis that the charge carriers are Cooper pairs witha finite phase coherence length due to the QPS.

[0148] Raman Spectroscopic Evidence for Superconductivity at 645 K inSingle-wall Carbon Nanotubes

[0149] Here the inventor analyzes the data of the temperature dependentfrequency shifts of the Raman active G-band in single-walled carbonnanotubes containing different concentrations of the magnetic impurityNi:Co. This data were recently obtained by Walter et al. at theUniversity of North Carolina [41]. The inventor shows that these datacan be quantitatively explained by the magnetic pair-breaking effect onsuperconductivity with a mean-field transition temperature of 645 K and2Δ/k_(B)T_(c0)=3.6. This is in excellent agreement with independentelectrical and single-particle tunneling data shown above.

[0150] It is known that Raman scattering has provided essentialinformation about the electron-phonon coupling and the electronic pairexcitation energy in the high-T_(c) cuprate superconductors [42, 43,44]. The anomalous temperature dependent broadening of the Raman activeB_(lg)-like mode of 90 K superconductors RBa₂Cu₃O_(7-y) (R is arare-earth element) allows one to precisely determine a superconductinggap at 2Δ=40.0±0.8 meV [43]. Moreover, it was found that the thresholdtemperature marking the softening of the B_(lg) mode with 2Δ<hω<2.2Δcoincides with T_(c), and the mode softens further for lowertemperatures. The pronounced softening observed only for the B_(lg) modeis due to the fact that the phonon energy of the B_(lg) mode is veryclose to 2Δ and the mode is strongly coupled to electrons [43, 45]. Itshould be emphasized that such a softening effect is observable only forthose phonon modes with their energies very close to 2Δ.

[0151] In FIG. 11A, the inventor plots the temperature dependence of thefrequency for the Raman-active B_(lg) mode of a 90 K superconductorYBa₂Cu₃O_(7-y). The figure is reproduced from Ref. 42. It is apparentthat the frequency decreases linearly with increasing temperature aboveT_(c)=90 K, and that the mode starts to soften below T_(c). Such atemperature dependence of the frequency above T_(c) is caused by thermalexpansion. The temperature dependence of the frequency will become morepronounced at higher temperatures since the magnitude of the slop−dlnω/dT is essentially proportional to the lattice heat capacity thatincreases monotonously with temperature. The significant softening ofthe mode below T_(c) occurs only if the energy of the Raman mode is veryclose to 2Δ and the electron-phonon coupling is substantial [44], as itis the case in the 90 K superconductor YBa₂Cu₃O_(7-y) [42, 43, 44]. Inorder to see more clearly the softening of the mode, I show in FIG. 11Bthe difference of the measured frequency and the linearly fitted curveabove T_(c). It is clear that the softening starts at T_(c) and thefrequency of the mode decreases by about 9 cm⁻¹ at 5 K.

[0152]FIG. 12 shows the temperature dependence of the frequency for theRaman active G-band of single-walled carbon nanotubes containingdifferent concentrations of the magnetic impurity Ni:Co. The data arefrom R. Walter et al. at the University of North Carolina [41]. It isremarkable that the frequency shows a clear tendency of softening belowabout 630 K in the sample with 0.2% Ni:Co impurity. Above 630 K, thefrequency decreases linearly with increasing temperature similar to thebehavior in YBa₂Cu₃O_(7-y) (FIG. 11A). The merging of the curves in FIG.12 at high temperatures suggests that the divergence of the curves atlow temperatures is not due to a difference in the mean chiralitydistribution of the nanotube bundle.

[0153] In order to see more clearly the softening of the mode, theinventor shows in FIG. 13 the difference between the measured frequencyand the linearly fitted curve above the kink temperatures (e.g., above630 K for the sample containing 0.2% Ni:Co). It is remarkable that theresults shown in FIG. 13 are similar to that shown in FIG. 11B. Thissuggests that the softening of the Raman active G-band in the SWNTs mayhave the same microscopic origin as the softening of the Raman activeBig mode in YBa₂Cu₃O_(7-y). This explanation is plausible only if thephonon energy of the G-band is very close to 2Δ. Indeed, the phononenergy of the G-band is 200 meV, very close to 2Δ=200 meV deduced fromthe tunneling spectrum and the electrical breakdown experiment.Therefore, it is very likely that the softening of the Raman activeG-band in the SWNTs is related to the superconducting transition.

[0154] From FIG. 13, one can clearly see that the softening starts atabout 632 K for the sample containing 0.2% Ni:Co, at about 617 K for thesample containing 0.45% Ni:Co, and at about 554 K for the samplecontaining 1.3% Ni:Co. By analogy to the result shown in FIG. 11B, theinventor can assign the mean-field transition temperature T_(c0)=632 K,617 K, and 554 K for the samples containing 0.2%, 0.45%, and 1.3% Ni:Co,respectively.

[0155] In FIG. 14, the inventor shows T_(c0) as a function of themagnetic impurity (Ni:Co) concentration. It is striking that T_(c0)decreases with increasing the magnetic concentration. The observedT_(c0) dependence on the magnetic concentration is very similar to thetheoretically predicted curve based on the magnetic pair-breaking effecton superconductivity [23]. This gives further support that the softeningof the Raman active G-band in the SWNTs is related to thesuperconducting transition around 600 K. Extrapolating to the zeromagnetic-impurity concentration, one finds T_(c0)=645 K. Using Δ=100 meVand T_(c0)=645 K, one calculates 2Δ/k_(B)T_(c0)=3.6, very close to thatexpected from the weak-coupling BCS theory. It is also remarkable thatthe magnitude of the gap deduced from the Raman data is in excellentagreement with that inferred from a tunneling spectrum.

[0156] It is known that the resistance of 1D superconductors is finitebelow the mean-field superconducting transition temperature T_(c0) dueto a large quantum phase slips [19]. In the smallest diameter SWNT withd=0.42 nm, the mean-field superconducting transition temperature T_(c0)was found to be about 15 K [46]. The temperature dependence of theresistance for the 1D superconductor is in good agreement with thetheoretical calculation [46]. In FIG. 15A, the inventor plots theresistance as a function of T/T_(c0) for the smallest diameter SWNT. Thedata are extracted from Ref. [46]. It is apparent that the resistanceincreases more rapidly above 0.5 T_(c0) and flattens out towards T_(c0).The resistance at T_(c0) appears to be about four times larger than thatat 0.5T_(c0). Below 0.5T_(c0), the temperature dependence of theresistance can be well fitted by a power law:R(1)=R_(o)+AT^({acute over (υ)}), as demonstrated in FIG. 15B. HereR_(o) is contributed from the contact resistance and the intrinsicresistance that arises from the quantum phase slips. From the fit, onefinds that the power β=1.77±0.18. The theory of quantum phase slips inquasi-1D superconductors [19] predicts that β=2μ-3, where μ is aquantity that characterizes the ground state. The resistance at zerotemperature can approach to zero when μ>2, but is finite when μ<2.Disorder can lead to weak localization of Cooper pairs and thus make μ<2[19].

[0157] In FIG. 16, the inventor shows temperature dependence of theresistivity for a SWNT rope. The data are extracted from Ref. 47. Below200 K, the resistivity is nearly temperature independent, which suggeststhat the measured resistance is contributed only from metallic SWNTs.Since the resistance for semiconducting chirality tubes is larger thanthat for metallic chirality tubes by several orders of magnitude [48],any current paths which include semiconducting chirality tubes are“shortened” by current paths which consist of only metallic chiralitytubes. Considering the fact that two thirds of the tubes havesemiconducting chiralities, the intrinsic resistivity of the metallicchirality tubes must be much smaller than that shown in FIG. 16. Thecontact barriers among the metallic chirality tubes may contribute tothe resistance that increases weakly with decreasing temperature. Thenearly temperature independent resistance observed below 200 K might bedue to the competing contributions of the barrier resistance and on-tubemetal-like resistance. Above 200 K, the resistivity increases suddenlyand starts to flatten out above 550 K. Such a temperature dependence ofresistivity is similar to that shown in FIG. 15A, and agrees withquasi-1D superconductivity at about 600 K.

[0158]FIG. 17 shows temperature dependence of resistance for asingle-walled nanotube with d=1.5 nm. The data are extracted from Ref.49. The distance between the two contacts is about 200 nm and thecontacts are nearly ideal with the transmission probability of about 1[49]. It is remarkable that the temperature dependence of the resistancecan be fitted by a power law R(T)=R_(o)+AT^({acute over (υ)}) withβ=1.71±0.23. The power β for the 1.5 nm SWNT is nearly the same as thatfor the 0.4 nm SWNT, which has been proved to be superconducting.Comparing FIG. 17 with FIG. 15, one could infer that T_(c0) for the 1.5nm SWNT is above 600 K. It should be mentioned that, within theFermi-liquid picture, both electron-phonon backscattering and umklappelectron-electron scattering lead to a resistivity which is linearlyproportional to temperature [50, 51]). Therefore, it is difficult toexplain the observed temperature dependence of the resistance if theSWNT were not a quasi-1D superconductor.

[0159] The data shown in FIG. 17 can also rule out Luttinger-liquidbehavior. Phonon backscattering in Luttinger-liquid leads tosemiconductor-like electrical transport at low temperatures andmetal-like transport with β<1 at high temperatures [52]. This is insharp contrast with the data shown in FIG. 17. Qualitatively, tunnelingspectra in both SWNT and MWNT agree with either the Luttinger-liquidtheory or the environmental Coulomb blockade theory [34, 53]. TheLuttinger-liquid theory [35] predicts that if α^(bulk)=0.37, thenα^(end) =0.94, where α^(bulk)/α^(end) is the exponent of power law intunneling spectrum for the electron tunneling into the bulk/end of theLuttinger-liquid. But experiments [34] showed that α^(bulk)=0.37 andα^(end)=0.6, in disagreement with the prediction of the Luttinger-liquidtheory. Moreover, recent calculation [54] shows that the Luttingerparameter in SWNTs remains close to its free fermionic values of 1, evenfor larger values of doping. This implies that α^(bulk)˜0. Thus, onlythe environmental Coulomb blockade theory is able to explain thetunneling data [34].

[0160] Now a question arises: What is the pairing mechanism responsiblefor such high superconductivity in carbon nanotubes, and why does thesmallest SWNT have such a low T_(c0)? A theoretical calculation showedthat superconductivity as high as 500 K can be reached through thepairing interaction mediated by acoustic plasmon modes in aquasi-one-dimensional electronic system [55]. The calculated T_(c) as afunction of the areal carrier density for InSb wires of the crosssections of 50 nm×10 nm and 80 nm×1 nm is re-plotted in FIG. 18. Thetheoretical calculation indicates that the highest T_(c) occurs at adoping level where the first 1D subband is nearly occupied, and thatsuperconductivity decreases rapidly with increasing the carrier density.This is because an increase of the carrier density raises the Fermilevel so that more transverse levels are involved, diminishing thequasi-1D character of the system. For a metallic single-walled nanotubewith d>1 nm, two degenerate 1D subbands are partially occupied by holecarriers with the carrier concentration in the order of 10¹⁹/cm³. Thisis the most favorable condition for achieving high-temperaturesuperconductivity within the plasmon-mediated mechanism [55]. On theother hand, the smallest SWNT has a carrier density of 3.4×10²³/cm³, asestimated from the measured penetration depth (3.9 nm) and the effectivemass of supercarriers (0.36 me) [46]. One can easily show that 8transverse subbands cross the Fermi level in the smallest SWNT, whichmakes the plasmon-mediated mechanism very ineffective. This cannaturally explain why the T_(c0) in the smallest SWNT is only 15 K.Interestingly, the value 2Δ/k_(B)T_(c0)=3.6 deduced for SWNTs is inremarkably good agreement with the theoretical prediction [55].

[0161] For multi-layer electronic systems such as cuprates and MWNTs,high-temperature superconductivity can occur due to an attraction of thecarriers in the same conducting layer via exchange of virtual plasmonsin neighboring layers [56]. Indeed a strong electron-plasmon coupling incuprates has been verified by well-designed optical experiments [57].For MWNTs, the dual characters of the quasi-one-dimensional andmulti-layer electronic structure could lead to a larger pairinginteraction and a higher T_(c0). It is interesting that the energy gap(pairing energy) in the carbon nanotubes is close to that (>60 meV) [58]for deeply underdoped cuprates that would exhibit phase-coherentsuperconductivity above room temperature if the effective mass ofcarriers in cuprates could be reduced by one order of magnitude.

EXAMPLES

[0162] The following examples are submitted to illustrate the benefitand uses of the embodiments taught herein, but not to limit the claimsto any one embodiment or application.

Example 1

[0163] The present invention is a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity whereby nested metallic chirality layers in MWNT areformed whereby the resistance can be tuned based on the number of nestedmetallic chirality layers—an increase in layers decreases resistivity(FIG. 19). The most phase coherent embodiment of the present examplesoccurs where all the nested layers have metallic chiralities and theintra-nested tube distance is as small as possible. This is due to aneffective increase in the number of the transverse channels by theJosephson coupling of adjacent superconducting layers. The resistancedecreases exponentially with increasing nested superconducting layers.The zero resistance or phase coherent state can be achieved in a singleMWNT that consists of nested superconducting layers that meet or surpassthe minimum number of nested layers to achieve high temperaturesuperconductivity.

Example 2

[0164] The present example is a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity whereby SWNTs are bundled by putting several metallicchirality SWNTs in parallel and packed adjacent to each other resultingin a much lower resistance than the sum of the individual tubes. FIG. 20shows a decrease in resistance with the configuration of the resultingbundles. The diameters of the SWNTs in the bundle are not necessarilyidentical. The preferred embodiment of this example occurs where theinter-tube distance is as close as possible. The Josephson couplingamong the tubes can suppress the QPS and lower the resistanceexponentially.

Example 3

[0165] The present example is a composition and method of obtainingphase-coherent or nearly phase-coherent high temperaturesuperconductivity whereby several phase-incoherent MWNTs are put inparallel and packaged in an adjacent configuration, the resulting bundlehas a much lower resistance than the sum of the individual tubes. FIG.21 shows the decrease in resistance with the configuration of the MWNTbundles. The diameters and the numbers of the adjacent superconductinglayers of the MWNTs are independent and need not be identical. Thepreferred embodiment of this example occurs where the inter-tubedistance is as close as possible. The Josephson coupling among the tubescan suppress the QPS thereby exponentially lowering the resistanceapproaching the zero resistance state.

Example 4

[0166] The present example is a composition and method of obtaining hightemperature superconductivity by combining the embodiments described inexample 2 and example 3 whereby a bundle of MWNTs and SWNTs arecombined.

Example 5

[0167] The present example is a composition and method of makingsuperconducting quantum interferences devices (SQUIDs) that can operateat room temperature and have superior spatial resolution. A SQUID can beconstructed from two phase-coherent superconducting MWNTs or from twophase-coherent superconducting carbon nanotube bundles by intertubecrossings, as shown in FIG. 22. Two phase-coherent superconducting MWNTsare preferred. The intertube crossings act as Josephson weak links.

[0168] Suitable suspending agents for use in this invention include,without limitation, polyvinyl alcohol, polyvinyl acetates, celluloseethers and finely divided inorganic powders in an appropriate solventsuch as water, alcohols, a hydrocarbon (alkyl, alkenyl, or aryl), achlorohydrocarbon (alkyl, alkenyl, or aryl), a chlorocarbon (alkyl,alkenyl, or aryl), a fluorohydrocarbon (alkyl, alkenyl, or aryl), achlorofluorohydrocarbon (alkyl, alkenyl, or aryl), a chlorofluorocarbon(alkyl, alkenyl, or aryl), a fluorocarbon (alkyl, alkenyl, or aryl) ormixtures or combinations thereof.

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[0228] All references cited herein are incorporated by reference as iffully reproduced. While this invention has been described fully andcompletely, it should be understood that, within the scope of theappended claims, the invention may be practiced otherwise than asspecifically described. Although the invention has been disclosed withreference to its preferred embodiments, from reading this descriptionthose of skill in the art may appreciate changes and modification thatmay be made which do not depart from the scope and spirit of theinvention as described above and claimed hereafter.

I claim:
 1. A composition comprising at least one nanotube, where the atleast one nanotube has a phase-coherent or phase incoherentsuperconductivity above 20 K.
 2. The composition of claim 1, wherein thesuperconductivity occurs above 120 K.
 3. The composition of claim 1,wherein the superconductivity occurs above 250 K.
 4. The composition ofclaim 1, wherein the superconductivity occurs above 300 K.
 5. Thecomposition of claim 1, wherein the nanotubes are selected from thegroup consisting of single-wall nanotubes, multi-walled nanotubes andmixtures or combinations thereof.
 6. The composition of claim 2, whereinthe nanotubes are single walled nanotubes and the superconductivity isphase-incoherent.
 7. The composition of claim 2, wherein the nanotubesare multi-walled nanotubes and the superconductivity is phase-coherent.8. The composition of claim 1, further comprising a bundle of nanotubes.9. The composition of claim 8, wherein the nanotubes are selected fromthe group consisting of single-wall nanotubes, multi-walled nanotubesand mixtures or combinations thereof.
 10. The composition of claim 9,wherein the nanotubes are single walled nanotubes and thesuperconductivity is phase-coherent.
 11. The composition of claim 9,wherein the nanotubes are multi-walled nanotubes and thesuperconductivity is phase-coherent.
 12. The composition of claim 1,further comprising a matrix including bundles of nanotubes.
 13. Thecomposition of claim 12, wherein the nanotubes are selected from thegroup consisting of single-wall nanotubes, multi-walled nanotubes andmixtures or combinations thereof.
 14. The composition of claim 13,wherein the nanotubes are single walled nanotubes and thesuperconductivity is phase-coherent.
 15. The composition of claim 13,wherein the nanotubes are multi-walled nanotubes and thesuperconductivity is phase-coherent.
 16. The composition of claim 1,further comprising nanotubes, nanotube bundles or mixtures orcombinations thereof.
 17. The composition of claim 1, wherein thenanotubes are capable of conducting current with minimal to no loss. 18.The composition of claim 1, wherein each nanotube includes an outer wallhaving a chirality of Mod3(n−m)=0.
 19. The composition of claim 1,wherein each nanotube includes an outer wall having a chirality ofn−m=0.
 20. The composition of claim 8, wherein each wall of eachnanotube has a chirality of Mod3(n−m)=0.
 21. The composition of claim 8,wherein each wall of each nanotube has a chirality of n−m=0.
 22. Thecomposition of claim 8, wherein the nanotubes are aligned along an axisand an inter-nanotube separation is between about 2.2 Å and about 5 Å.23. The composition of claim 8, wherein the nanotubes are aligned alongan axis and an inter-nanotube separation is between about 2.5Å and about4 Å.
 24. The composition of claim 8, wherein the nanotubes are alignedalong an axis and an inter-nanotube separation is between about 2.5 Åand about 3.5 Å.
 25. The composition of claim 8, wherein the nanotubesare aligned along an axis and an inter-nanotube separation is betweenabout 2.75 Å and about 3.25 Å.
 26. The composition of claim 1, whereinthe composition is formed into an electrically conducting element, arope, or a wire.
 27. The composition of claim 1, wherein the compositionis deposited on a metallic surface.
 28. The composition of claim 1,further comprising sufficient dopant to support superconductivity. 29.The composition of claim 28, wherein the dopant is selected from thegroup consisting of a surface having a different work function, anelectric field, a chemical dopant, and a physical dopant.
 30. Thecomposition of claim 1, wherein the chemical and physical dopants areselected from the group consisting of oxidants, reductants, dopantsresulting from atom or ion implantation, and dopants from chargedparticle bombardment.
 31. An apparatus comprising a component includinga composition claims 1-30.
 32. The apparatus of claim 31, furthercomprising at least two electronic components interconnected with thecomposition.
 33. The apparatus of claim 31, wherein the apparatuscomprises a levitation apparatus comprising superconducting magnetscomprising the composition.
 34. The apparatus of claim 31, wherein thecomponent includes an electrically conductive element.
 35. The apparatusof claim 31, wherein the apparatus comprises magnetic reading heads,magnetic switch devices, magnetic imaging devices or superconductingquantum interference devices.
 36. A method for forming superconductingmaterials comprising the steps of: providing a composition includingsuperconducting nanotubes, superconducting nanotube bundles or mixturesor combinations thereof, aligning the superconducting nanotubes,superconducting bundles or mixtures or combinations thereof and formingthe aligned superconducting nanotubes, superconducting nanotube bundlesor mixtures or combinations thereof into an elongate form.
 37. Themethod of claim 36, further comprising the step of: doping the elongateform with sufficient dopant so that the form superconducts at a desiredtemperature.
 38. The method of claim 36, the desired temperature isabove 20 K.
 39. The method of claim 36, the desired temperature is above120 K.
 40. The method of claim 36, the desired temperature is above 250K.
 41. The method of claim 36, the desired temperature is above 300 K.42. A method for forming superconducting materials comprising the stepsof: providing a suspension of a composition including superconductingnanotubes, superconducting nanotube bundles or mixtures or combinationsthereof in a solvent; and forcing the suspension through an smallorifice onto a substrate, where the forcing cause an alignment of thesuperconducting nanotubes, superconducting bundles or mixtures orcombinations thereof on the substrate.
 43. A method for formingsuperconducting connection between electronic contacts comprising thesteps of: providing a suspension of a composition includingsuperconducting nanotubes, superconducting nanotube bundles or mixturesor combinations thereof; and spraying the suspension onto a substratehaving electronic contacts disposed thereon so that the compositionforms an electrically conductive pathway between a desired pair ofcontact along a desired path, where the spraying aligns thesuperconducting nanotubes, superconducting bundles or mixtures orcombinations thereof.